Original Research Article

Percent Excess Weight Loss (%EWL) or Percent Excess Body Mass Index Loss (%EBMIL)? Determination of a conversion factor to unify the two formulas

Dr.Antonio Martin-Duce,

Nieves Gonzalez1, Felicidad Lopez2 and Antonio Martín-Duce3

1Renal, Vascular and Diabetes Research Laboratory, Fundacion Instituto de Investigación Sanitaria-Fundación Jiménez Díaz (IIS-FJD), Autonoma de Madrid Spanish Biomedical Research in Diabetes and Associated Metabolic Disorders (CIBERDEM) Madrid, Spain.
2 Department of Nursery, Foundation Jiménez Diaz. Madrid, Spain.
3Department of Nursery, Faculty of Medicine and Health Sciences, Alcalá University. Madrid, Spain.

The reality today is the frequent application of the percent of excess weight loss (%EWL) formula requiring the use of the complex concept of ideal weight. Whereas, the percent of excess body mass index loss (%EBMIL) formula

*Corresponding author:

Dr. Antonio Martín-Duce

E-mail: martinduce@gmail.com

 

Background: The reality today is the frequent application of the percent of excess weight loss (%EWL) formula requiring the use of the complex concept of ideal weight. Whereas, the percent of excess body mass index loss (%EBMIL) formula, advocated as the best equation for reporting results in bariatric surgery, aims to avoid it. Absolute values are most frequently used in medical patients, while the relative measures are used with surgical patients, being necessary to determine a reference value, ideal weight or ideal body mass index, with which to perform the calculation.

Objective: The aim of this study is to obtain a simple mathematical factor, which will allow the correlation of the two most common equations used for the presentation of the results of weight loss ─%EWL and %EBMIL─.

Methods: Based on the mathematical definition of %EWL, the concepts of Beginning weigh, Follow-up weight and Ideal Weight, and following the Guidelines of Metropolitan Insurance Company of 1983 –ideal weights is equivalent to a BMI of 22.0, in male and 20.8 in female-, a factor for each of the sexes was obtained: (%EBMIL)/(%EWL)=(BMIb-22.0)/(BMIb-25.0) and (%EBMIL)/(%EWL)=(BMIb-20.8)/(BMIb-25.0).

Results: A simple conversion factor (F) between the two formulas has been resulted. This numerical factor provides immediate and almost exact correlation, between both the formulas. %EBMIL=F x %EWL. To better assist the medical and scientific communities, this article includes a table with the Body Mass Index (BMI) initially spaced 0.5 units, also adding the gender specification, and the F already calculated.

Conclusions: A conversion factor to unify %EWL and %EBMIL has been determined, which facilitate the presentation and understanding of the results of weight loss in publications related to obesity surgeries and international conferences.

Keywords: Obesity; Weight Loss; Body Mass Index  Running title: Conversion factor for %EWL and %EBMIL.

Currently, obesity is a health-related, social and economic problem of the top priority in the world; most specifically in the West. There is a wide range of ongoing medical resources to combat this growing epidemic problem. The results have been historically used in a variety of measures, including 3 absolute ones: a) the number of units of weight lost, b) the percent of weight lost, and c) the percent of body mass index lost; and additionally 2 relative measures: d) the percent of excess weight loss (% EWL), and e) the percent of excess body mass index loss (% EBMIL). Although the absolute values are most frequently used in medical patients, the relative measures are used with surgical patients, being necessary to determine a reference value, ideal weight or ideal body mass index, with which to perform the calculation.


For many years, there has been an intense discussion about the concept of ideal weight 1, 2; both for drug dosage calculations, and for the surgical treatment of morbid obesity. The Ideal Body Weight (IBW) was proposed and accepted, by the Metropolitan Insurance Company (MIC) to describe a weight ranges associated with the maximum life expectancy3. For years, it has been the global benchmark for this parameter, despite the significant flaws it shows, both 1) in the selection of study groups: minimal representation of social minorities and lower income groups, exclusion of individuals with serious diseases, low age range (25-29); and 2) in the methodology: 10% of weight ranges were referred by telephone, with patients dressed  when  weighed, exclusion of individuals diagnosed with severe diseases (diabetes mellitus, oncological disorders, heart conditions), and the existence of three subgroups: small, medium and large scope. The latter variable, also introduces a subjective factor, which hinders the accurate inclusion of patients in one subgroup. This adds complexity, to the development of accurate tables, even to a greater extent. 


Therefore, gradually, studies have been conducted to find new formulas with more variables, to facilitate this objective determination of a simpler form 4-9. However, the mathematical difficulties, which such schemes entailed ─with the dispersion of ideal weights for the same height obtained─, led to in a true anarchy in the presentation of these results. This fact made the proper comparison among the different published studies, extremely complicated. 


Moreover, in an attempt to objectify and simplify the matter, updates in the old concept of Body Mass Index (BMI) described by the mathematician Adolphe Quetelet in 1835 (ref. 10), have been carried out. Quetelet calculated BMI as the ratio between weight and height2 in males, and weight / height in females; but later was modified for mathematical calculations sake convenience as weight / height2 for both sexes 11. The BMI has gained remarkable popularity, for its excellent correlation with body density and skinfold thickness measurements, and also for its mathematical simplicity. However, BMI shows a weak point, which hinders the comparative analysis. Due to the scanty number of patients included in the studies of morbidity and mortality, the ideal BMI is not a single value, but rather a range between 20 and 25 kg/m2


The use of BMI is limited. BMI has not included relevant factors –anthropometric features or the percentage of fat–. The addition to the clinic of simple parameters such as the waist-to-hip ratio index and waist circumference, have proved very useful, since they provide evidence that the distribution of fat is a crucial predictor of metabolic abnormalities and cardiovascular risk 12. Moreover, body fat content estimated by skinfold (PT), bioelectric impedance (BIA) and dual X-ray absorptiometry (DEXA), isotope dilution and computerized tomography, have been also added to the list of tools for the monitoring of obesity 13, 14. However, the disadvantage of the waist circumference variation is that it cannot distinguish visceral adipose tissue and abdominal tissue located subcutaneously; while electric, radioactive and imaging techniques are expensive, are not generally available, require qualified personnel and are difficult to standardize both the equipment and the observers. 


The BMI did not directly measure fat, but it has a direct correlation with measurements of body fat 15, being a more simple and economical medical alternative, widely used.


Having thus stated the above situation, we are currently working on the wide disparity displayed in the calculated reported weight loss, obtained by different mathematical formulas 16, 17. Undoubtedly, given the vast differences, in the initial weight and subsequent weight loss, among patients operated on for morbid obesity, the most accurate approach is to present the results as follow:


Percent Excess Weight Loss (%EWL) = [(Beginning Weight ─ Follow-up Weight) / Beginning Weight ─ Ideal Weight)] x 100


Percent Excess Body Mass Index Loss (%EWBIL) = [(Beginning BMI ─ Follow-up BMI) / Beginning BMI ─ Ideal BMI)] x 100

Based on the ideal weight data tables provided by the MIC, which are the ones most frequently used by the scientific community, the %EWL could be calculated. A single value of ideal BMI for the %EBMIL remains to be determined, and subsequently to achieve a mathematical formula, which would allow to easily correlate the two equations.


In the Guidelines of the MIC, the value of the ideal weight for a medium scope corresponds to an average BMI of 22.0 in males, and 20.8 in females 18. Meanwhile, Lemmens et al. obtained a value of 22.0 for both the sexes, as an average of the different formulas accepting the ideal weight 19. Following the recommendations of Pi Sunyer, endorsed by numerous experts 16, 20, 21, the studies expressing their results as %EBMIL, used 25.0 as the unique value of ideal BMI for both the sexes. Consequently, these different approaches make a direct comparison between the %EWL and %EBMIL quite problematic. It is, therefore, necessary to achieve a mathematical solution, which will allow the correlation of both the formulas.
 

Objective:

The aim of this study is to obtain a simple mathematical factor, which will allow the correlation of the two most common equations used for the presentation of the results of weight loss ─%EWL and %EBMIL─, in publications related to obesity surgeries and international conferences. The discovery of a single conversion factor will favor the comparison of the results among the different groups.

Initially, each of the factors of the %EWL formula are divided by size squared (H) 2:

Clyto Access

Following the Guidelines of Metropolitan Insurance Company of 1983, it is found that the ideal weights referred for a medium frame is equivalent to a BMI of 22.0, in male and 20.8 in female 18. Therefore, %EWL can also be expressed as follows:


Clyto Access

 

If it is considered 25.0 as the ideal Body Mass Index for both the sexes, it is obtained:

 


Clyto Access


Clyto Access


Clyto Access

To better assist the medical and scientific communities, this article includes a table with BMI initially spaced 0.5 units, also adding the gender specification, and the calculated F in both the sexes.

Table 1 shows the values of F in both the sexes, for different values of initial BMI. Table 1 Conversion factor (F) according to beginning BMI in males and females.

Beginning

BMI (kg/m2)

F

(males)

F

(females)

Beginning

BMI (kg/m2)

F

(males)

F

(females)

Beginning

BMI (kg/m2)

F

(males)

F

(females)

80

1.054

1.076

64.5

1.076

1.106

49

1.122

1.171

79.5

1.055

1.077

64

1.077

1.108

48.5

1.125

1.175

79

1.056

1.078

63.5

1.078

1.109

48

1.128

1.179

78.5

1.056

1.078

63

1.079

1.110

47.5

1.130

1.182

78

1.057

1.079

62.5

1.080

1.112

47

1.133

1.187

77.5

1.057

1.080

62

1.081

1.113

46.5

1.136

1.191

77

1.058

1.081

61.5

1.082

1.115

46

1.139

1.195

76.5

1.058

1.081

61

1.083

1.117

45.5

1.143

1.200

76

1.059

1.082

60.5

1.084

1.118

45

1.146

1.205

75.5

1.059

1.083

60

1.086

1.120

44.5

1.150

1.221

75

1.060

1.084

59.5

1.087

1.122

44

1.154

1.215

74.5

1.061

1.085

59

1.088

1.123

43.5

1.158

1.221

74

1.061

1.086

58.5

1.090

1.125

43

1.162

1.227

73.5

1.062

1.087

58

1.091

1.127

42.5

1.167

1.233

73

1.062

1.087

57.5

1.092

1.129

42

1.171

1.240

72.5

1.063

1.088

57

1.094

1.131

41.5

1.176

1.247

72

1.064

1.089

56.5

1.095

1.133

41

1.182

1.262

71.5

1.064

1.090

56

1.097

1.135

40.5

1.187

1.271

71

1.065

1.091

55.5

1.098

1.138

40

1.193

1.280

70.5

1.066

1.092

55

1.100

1.140

39.5

1.200

1.290

70

1.067

1.093

54.5

1.102

1.142

39

1.207

1.300

69.5

1.067

1.094

54

1.103

1.145

38.5

1.214

1.311

69

1.068

1.095

53.5

1.105

1.147

38

1.222

1.323

68.5

1.069

1.096

53

1.107

1.150

37.5

1.231

1.336

68

1.070

1.098

52.5

1.109

1.153

37

1.240

1.350

67.5

1.071

1.099

52

1.111

1.155

36.5

1.250

1.365

67

1.071

1.100

51.5

1.113

1.158

36

1.261

1.382

66.5

1.072

1.101

51

1.115

1.161

35.5

1.272

1.400

66

1.073

1.102

50.5

1.118

1.165

35

1.286

1.420

65.5

1.074

1.104

50

1.120

1.168

 

 

 

65

1.075

1.105

49.5

1.122

1.106

 

 

 



BMI: (Body Mass Index)

The aim of this study was to obtain a simple conversion factor between the two formulas, which considered different variables ─Ideal BMI and Ideal Weight─, as a benchmark for determining the weight lost. This reality induced a wide dispersion in the data presentation toward the scientific community, making it problematic to compare the results of the different studies.  Although the trend of surgical specialists is to use and recommend %EBMIL16, 20, 22-24; the evaluation of the recent scientific literature, points out the evidence that the use of the %EWL is much more frequent than %EBMIL formula. In detail, 80.3% of the abstracts presented at the 14th World Congress of International Federation for the Surgery of Obesity (IFSO) reporting a weight loss method, used the %EWL (n = 53), while only in 19.7% (n = 13) %EBMIL was used 19. The circumstances of %EWL based not only on a unique ideal weight, but divided into 3 different scopes, triggers subjectivity in the process of selection performed by the researcher, which leads to comparative errors, and therefore, makes its use questionable. 

Within this scenario, the recommendation is that %EBMIL should always be used. For the determination of the %EWL the mid-point of the range of the majority body scope (the medium) should be chosen, which corresponds to a BMI of 22.0 in males and 20.8 in females; although the authors recommend to follow the conclusions of the studies of Lemmens et al., where the value of BMI is 22.0 for both the sexes. Subsequently, using the conversion factor "F", the determination of %EBMIL will be extremely simple. The resulting dispersion in the minority cases of small and large scopes will be minimal and irrelevant. While the ideal BMI is more relevant in a range of 20-25 kg/m2, than with a single absolute value, it is necessary to consider each of the individual human characteristics (age, sex, race, scope ...). 

It is highly recommended that for the determination of the value of %EBMIL, scientists should fix the value 25.0 (upper limit) in all patients, regardless of its accuracy 22,23. A specific case to consider is the existence, as indicated by Ko etal. of an early associated morbidity into obese patients with Asian origin, stooping in them the ideal BMI in 22.0, which coincides with the %EWL and the %EBMIL 24. In this case the conversion factor should not be necessary.

In conclusion, a conversion factor to unify %EWL and %EBMIL has been determined, which will provide immediate and almost exact correlation, between the two formulas, and facilitate the presentation and understanding of the results of weight loss ─%EWL and %EBMIL─, in publications related to obesity surgeries and international conferences.

The authors thank Marcin Koza for proofreading the manuscript.

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Received: 30 November 2016

Accepted: 13 January 2017

Published: 30 January 2017

Reviewed By : Dr. Laura McArthur.Dr. Deng-Fu Guo.Dr. Jian-Hua Zhang.Dr. Nikolaos Papanas.

Copyright:

Copyright: Copyright: © 2017 Dr. Antonio Martín-Duce. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.